Elementary Linear Algebra 7th Edition

$|A|=6$ and $|A^{-1}|==\frac{1}{6}$.
Let $A$ be given by $$A=\left[ \begin {array}{cccc} 1&-1\\ 2&4 \end {array} \right] ,$$ then we have $A^{-1}=\frac{1}{6}\left[ \begin {array}{cccc} 4&1\\ -2&1 \end {array} \right]$. Now, $|A|=6$ and $|A^{-1}|=\frac{1}{6^2}6=\frac{1}{6}$. Hence, we verify that $$|A^{-1}=\frac{1}{|A|}.$$